It's one of the most common phrases in daily life—and one of the most misunderstood. This is an interactive exploration of probability through six different lenses.
Imagine 100 versions of today. In how many does it rain?
Run the same day 10 times and watch randomness unfold.
30% of the forecast area will experience rain.
Probability is the long-run frequency of an event in repeated trials.
Probability is your rational degree of belief, updated by evidence.
Probability is a real physical property—a tendency in the world.
When a meteorologist says "30% chance of rain," they typically mean: given conditions like these, rain occurs about 30% of the time. But the deeper question—what is probability itself?—has occupied philosophers and statisticians for centuries. The three main camps (frequentist, Bayesian, propensity) give the same number fundamentally different meanings.
Imagine 100 parallel versions of today, all with identical conditions. A 30% chance means rain falls in about 30 of them.
Each square is one possible version of today. The green squares are the realities where you'd need an umbrella. The rest? You'd be fine without one. This is the most intuitive way to think about probability: as a fraction of possible outcomes.
A 30% chance doesn't mean it will rain 30% of the day. It means that out of many days with these exact conditions, about 3 in 10 would see rain. Run the simulation multiple times—sometimes you'll get 5 rainy days, sometimes only 1. That's randomness.
If today repeated 100 times, rain would fall on about 30 of them.
About 30% of the forecast area will experience rain at some point today.
30% means: if we repeated this exact situation infinitely many times, rain would occur in 30% of those instances. Probability is an objective property of repeatable events—it exists in the world, not in our heads.
For frequentists, probability is not a degree of belief—it's an objective fact about the world. A 30% chance of rain means that this type of weather system, under these exact conditions, produces rain in 30% of cases.
The limitation: This only works for repeatable events. What's the probability that Caesar crossed the Rubicon? A frequentist would say the question is meaningless—it only happened once. You can't have a frequency of a singular event.
30% represents how confident you should be that it will rain, given everything you know. It's subjective but rational—and it updates as you learn new things.
For Bayesians, probability is personal but not arbitrary. Your 30% might differ from mine if we have different information. As new evidence arrives, we rationally update our beliefs using Bayes' theorem.
This interpretation can handle one-time events. "What's the probability this startup succeeds?" is a perfectly meaningful question—it's your rational degree of confidence given what you know.
30% describes the atmosphere's actual disposition to produce rain—a real property of the physical system itself, not just our knowledge of it.
Propensity theorists (like Karl Popper) argue that probability is a real, physical property—like mass or charge. The atmosphere doesn't just "happen to rain 30% of the time"—it has a genuine tendency, a disposition, a propensity of 0.3 to produce rain.
Unlike frequentism, this applies to single events. Unlike Bayesianism, it's objective—it exists in the world, not in our heads. The propensity is as real as the temperature or the pressure.
The same number means fundamentally different things depending on your philosophy of probability.
In the long run, under identical conditions, rain occurs 30% of the time. This is an objective fact about repeatable events.
Can't handle singular events. "What's the probability Caesar crossed the Rubicon?" is meaningless.
Given everything I know, I'm 30% confident it will rain. This updates as I learn new information.
Subjective—different people can rationally hold different probabilities. Some find this troubling.
The physical system has a 0.3 tendency to produce rain. This is a real property, like mass or charge.
Hard to verify directly. How do you measure a "tendency" other than by frequency?
For everyday decisions, the interpretation matters less than the number. A 30% chance means rain is possible but unlikely. A 70% chance means rain is likely but not guaranteed. The key insight: probability is not certainty. Always consider the consequences of being wrong in either direction—bringing an umbrella you don't need is usually less costly than getting soaked.